scalar surfaceOptimizer::optimiseSteepestDescent(const scalar tol)
{
point& pOpt = pts_[trias_[0][0]];
//- find the bounding box
const scalar avgEdge = Foam::mag(pMax_ - pMin_);
//- find the minimum value on the 5 x 5 raster
scalar K = evaluateStabilisationFactor();
scalar funcBefore, funcAfter(evaluateFunc(K));
//- start with steepest descent optimisation
vector gradF;
tensor gradGradF;
vector disp;
disp.z() = 0.0;
direction nIterations(0);
do
{
funcBefore = funcAfter;
evaluateGradients(K, gradF, gradGradF);
//- store data into a matrix
matrix2D mat;
mat[0][0] = gradGradF.xx();
mat[0][1] = gradGradF.xy();
mat[1][0] = gradGradF.yx();
mat[1][1] = gradGradF.yy();
FixedList<scalar, 2> source;
source[0] = gradF.x();
source[1] = gradF.y();
//- calculate the determinant
const scalar det = mat.determinant();
if( mag(det) < VSMALL )
{
disp = vector::zero;
}
else
{
disp.x() = mat.solveFirst(source);
disp.y() = mat.solveSecond(source);
if( mag(disp) > 0.2 * avgEdge )
{
vector dir = disp / mag(disp);
disp = dir * 0.2 * avgEdge;
}
}
# ifdef DEBUGSmooth
Info << "Second gradient " << gradGradF << endl;
Info << "Gradient " << gradF << endl;
Info << "Displacement " << disp << endl;
Info << "K = " << K << endl;
# endif
pOpt -= disp;
K = evaluateStabilisationFactor();
funcAfter = evaluateFunc(K);
if( mag(funcAfter - funcBefore) / funcBefore < tol )
break;
#ifdef DEBUGSmooth
Info << "New coordinates " << pOpt << endl;
# endif
} while( ++nIterations < 100 );
return funcAfter;
}
// Implementation of knupp metric untangling
void knuppMetric::optimizeNodePosition(const scalar tolObsolete)
{
if( !bb_.contains(p_) )
p_ = 0.5 * (bb_.min() + bb_.max());
const scalar tol = Foam::sqr(2.0 * SMALL) * magSqr(bb_.min() - bb_.max());
label iterI, outerIter(0);
vector gradF, disp;
tensor gradGradF;
scalar func, lastFunc;
# ifdef DEBUGSmooth
forAll(normals_, nI)
{
const scalar fx = normals_[nI] & (p_ - centres_[nI]);
Info << "Tet " << nI << " has distance " << fx << " func "
<< Foam::sqr(mag(fx) - fx) << endl;
}
Info << "BoundBox size " << (bb_.max() - bb_.min()) << endl;
Info << "Tolerance " << tol << endl;
# endif
bool finished;
do
{
finished = true;
lastFunc = evaluateMetric();
iterI = 0;
do
{
# ifdef DEBUGSmooth
Info << "Iteration " << iterI << endl;
Info << "Initial metric value " << lastFunc << endl;
# endif
//- store previous value
const point pOrig = p_;
//- evaluate gradients
evaluateGradients(gradF, gradGradF);
//- calculate displacement
const scalar determinant = det(gradGradF);
if( determinant > SMALL )
{
disp = (inv(gradGradF, determinant) & gradF);
for(direction i=0;i<vector::nComponents;++i)
{
const scalar& val = disp[i];
if( (val != val) || ((val - val) != (val - val)) )
{
disp = vector::zero;
break;
}
}
p_ -= disp;
func = evaluateMetric();
# ifdef DEBUGSmooth
Info << "Second grad " << gradGradF << endl;
Info << "inv(gradGradF, determinant) " << inv(gradGradF, determinant) << endl;
Info << "Gradient " << gradF << endl;
Info << "Determinant " << determinant << endl;
Info << "Displacement " << disp << endl;
Info << "New metric value " << func << endl;
# endif
scalar relax(0.8);
label nLoops(0);
while( func > lastFunc )
{
p_ = pOrig - relax * disp;
relax *= 0.5;
func = evaluateMetric();
if( func < lastFunc )
continue;
//- it seems that this direction is wrong
if( ++nLoops == 5 )
{
p_ = pOrig;
disp = vector::zero;
func = 0.0;
}
}
lastFunc = func;
}
else
{
disp = vector::zero;
}
} while( (magSqr(disp) > tol) && (++iterI < 10) );
if( (lastFunc < VSMALL) && (evaluateMetricNoBeta() > VSMALL) )
{
beta_ /= 2.0;
finished = false;
}
} while( !finished && (++outerIter < 5) );
# ifdef DEBUGSmooth
Info << "Last value " << lastFunc << endl;
Info << "Beta " << beta_ << endl;
Info << "Metric with no beta " << evaluateMetricNoBeta() << endl;
forAll(normals_, nI)
{
const scalar fx = normals_[nI] & (p_ - centres_[nI]);
Info << "Tet " << nI << " has distance " << fx << " func "
<< Foam::sqr(mag(fx) - fx) << endl;
}
//::exit(1);
# endif
}
